wulfric.cell.SC_RHL#

wulfric.cell.SC_RHL(a: float, alpha: float)[source]#

Constructs primitive rhombohedral cell as defined in [1].

\[\begin{split}\begin{matrix} \boldsymbol{a}_1 &=& (a\cos(\alpha / 2), &-a\sin(\alpha/2), &0)\\ \boldsymbol{a}_2 &=& (a\cos(\alpha / 2), &a\sin(\alpha/2), &0)\\ \boldsymbol{a}_3 &=& \left(\dfrac{\cos\alpha}{\cos(\alpha/2)}\right., &0, &\left.a\sqrt{1 - \dfrac{\cos^2\alpha}{\cos^2(\alpha/2)}}\right) \end{matrix}\end{split}\]

Input values are used as they are, therefore, the cell might not be a standard primitive one.

Parameters:

afloat: Length of the lattice vectors of the conventional cell.
alphafloat: Angle between vectors \(a_2\) and \(a_3\) of the conventional cell in degrees.

Returns:

cell(3, 3) numpy.ndarray

Matrix of a primitive cell, rows are interpreted as vectors.

cell = [
    [a1_x, a1_y, a1_z],
    [a2_x, a2_y, a2_z],
    [a3_x, a3_y, a3_z],
]

References

[1]

Setyawan, W. and Curtarolo, S., 2010. High-throughput electronic band structure calculations: Challenges and tools. Computational materials science, 49(2), pp. 299-312.

Examples

>>> import wulfric
>>> wulfric.cell.SC_RHL(a=3, alpha=40)
array([[ 2.81907786, -1.02606043,  0.        ],
       [ 2.81907786,  1.02606043,  0.        ],
       [ 2.44562241,  0.        ,  1.73750713]])